Graphical Analysis In Exercises 9–12, match the P-value or z-s...

Question

Graphical Analysis In Exercises 9–12, match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning.

P= 0.2802

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Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says determine the p-value corresponding to the combined shaded regions under the standard normal distribution shown below. And below the text, we have our standard normal distribution with two shaded regions. The first shaded region is to the left of Z equal to -1.29, and the other shaded region is to the right of Z equals to 1.29. And we're also given four possible choices as our answers. For choice A, we have 0.8030. For choice B, we have 0.1970. For choice C, we have 0.0985, and for choice D, we have 0.9015. Now, we're asked to find the P-value corresponding to the combined shaded regions under the standard normal distribution shown in our graph. And our shaded regions correspond to the cumulative probability for Z less than -1.29, and the cumulative probability for Z greater than 1.29. So we can actually use uh the standard normal distribution table in order to find those probabilities. So, for Z equal to -1.29, We look up in our tables, we'll see that the cumulative probability P. Of Z less than minus 1.29. is going to be equal to 0.0985. And since our standard normal distribution is symmetric by symmetry, we know that the cumulative probability P of Z greater than 1.29 is also going to be equal to 0.0985. So to find the P-value corresponding to the combined shaded region, We'll just need to add these two probabilities together. So, our P value is going to be equal to the cumulative probability E. Of Z less than minus 1.29. Or greater than 1.29. So, this probability is just going to be equal to the sum of the two probabilities that we found earlier. So this is going to be equal to 0.0985. Plus 0.0985 and we add those two values together. We see that our P value is going to be equal to 0.1970. So that is the answer that we're looking for for this problem. And if we compare that to our answer choices, we see that the correct answer choice corresponds to answer choice B. So I hope that this explanation has been useful, and I'll see you in the next video.

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Graphical Analysis In Exercises 9–12, match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning.

P= 0.2802

Key Concepts

P-value

Z-statistic

Normal Distribution

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Graphical Analysis In Exercises 9–12, match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning.P= 0.2802